i think that you can get him off the bridge with your sword but ia am not sure and make sure that you have your bombs equipped to your arowws. but if you are having trouble finding more arrows just go around cutting up the grass and you will most likely find some.

well this is the guy that has shields on each side and you need arrows to kill him. this is the second monster you have to beat on the bridge not the first. and I have tried for the live of me to cut grass and get arrows and it aint happenin.